{"paper":{"title":"Strings of congruent primes in short intervals II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tristan Freiberg","submitted_at":"2011-10-30T17:13:59Z","abstract_excerpt":"Let $p_1 = 2, p_2 = 3,...$ be the sequence of all primes. Let $\\epsilon$ be an arbitrarily small but fixed positive number, and fix a coprime pair of integers $q \\ge 3$ and $a$. We will establish a lower bound for the number of primes $p_r$, up to $X$, such that both $p_{r+1} - p_{r} < \\epsilon \\log p_r$ and $p_{r} \\equiv p_{r+1} \\equiv a \\bmod q$ simultaneously hold. As a lower bound for the number of primes satisfying the latter condition, the bound we obtain improves upon a bound obtained by D. Shiu."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6624","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}